Strong laser field ionization of Kr: first-order relativistic effects defeat rescattering

We have studied the ionization process of Kr atoms in strong laser fields by measuring the laser intensity dependence of highly charged ion yields. The measurements have been performed in an intensity regime between 10(16) W cm(-2) and 10(18) W cm(-2), which covers the transition from a nonrelativistic to a relativistic regime. While it is reasonable to assume that the initial tunnelling ionization process is well described nonrelativistically, the continuum dynamics of the photoelectrons change significantly. In particular, it has been found that the rescattering mechanism, which is dominant for lower charge states at low intensity, is largely diminished. We discuss three possible reasons: a decreasing cross section for electron impact ionization for higher charge states, an increasing spatial spread of the returning electronic wavepacket and the growing importance of the magnetic field component, which pushes the returning electron away from the core. Including these effects in the ionization rates based on the Ammosov, Delone and Krainov (ADK) tunnelling theory, we solve rate equations to predict ion yields, which agree with our experimental data.